Determining properties of magnetic elements

ABSTRACT

A method of determining differing characteristics of magnetic dipole elements such as orientation, coercivity, bias and response amplitude and a tag reader for reading magnetic tags containing such elements. The elements are scanned by a rotating magnetic field and two sets of transition data are determined. The transition data sets are associated with respective elements and analyzed to determine mean field values resolved along the element vectors. These field values are used to determine properties of the elements, such as coercivity.

FIELD OF THE INVENTION

[0001] This invention relates to magnetic elements, particularly but notexclusively to s methods of distinguishing between magnetic elements andmethods and apparatus for reading magnetic data tags which include oneor more magnetic elements, each of which can differ in coercivity,saturated dipole moment (i.e. response amplitude), orientation and biasfield.

BACKGROUND

[0002] Co-pending PCT publication number W099/35610 describes tags andreader systems primarily intended for tags fabricated from magneticmaterial of low coercivity, with elements at different orientations, inwhich data is recorded primarily by means of the orientation of theelements with respect to each other. The described system assumes thatthe coercivities of the tag elements are all the same, and are verysmall compared to the interrogation field.

SUMMARY OF THE INVENTION

[0003] According to the invention, there is provided a method of readinga magnetic tag having at least one magnetic element, comprisinginterrogating the tag with a scanning magnetic field, determiningtransition data associated with changes in the magnetisation state ofthe at least one magnetic element, associating the transition data withone or more respective elements; and for each element, determining theelement direction which corresponds to the transition data for thatelement.

[0004] Preferably, the element direction is determined by selecting thedirection that minimises the scatter of the transition field vectorsresolved along the direction of the element.

[0005] The transition data for each element can be grouped into twosets, which can be referred to as forward and reverse transitions. Allthose in the forward transition group have a positive component of thefield vector dH/dt along the element vector, and all those in thereverse group have a negative component of dH/dt along the elementvector. Mean field values, resolved along the element vector, can becalculated. The coercivity of the element is then calculated as half thedifference between the forward and reverse mean values, and the biasfield along the element is calculated as the sum of the forward andreverse mean values.

[0006] According to the invention, there is further provided a method ofdistinguishing between a plurality of magnetic elements, comprising thesteps of applying a scanning magnetic field to the elements, determiningthe direction of each of the elements, for each of the elements,determining the components of the field in the direction of the elementat which the element switches magnetisation states; and from saidcomponents, determining, for each of the elements, respectivecharacteristics of the element.

[0007] The invention further provides a method of determining, for amagnetic element, any one or more of a plurality of characteristicscomprising the coercivity of the element, the local magnetic field biasresolved in the direction of the element and the orientation of theelement, comprising the steps of applying a varying magnetic field tothe element, determining the direction of the element, determining thecomponents of the field in the direction of the element at which theelement switches magnetisation states; and from said components,determining the one or more characteristics of the element.

[0008] According to the invention, there is also provided a magnetic tagreader for reading a magnetic tag having at least one magnetic element,comprising means for interrogating the tag with a scanning magneticfield, means for determining transition data associated with changes inthe magnetisation state of the at least one magnetic element, means forassociating the transition data with one or more respective elements;and means for determining, for each element, the element direction whichcorresponds to the transition data for that element.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Embodiments of the invention will now be described, by way ofexample, with reference to the accompanying drawings, in which:

[0010]FIG. 1 is a schematic diagram of a magnetic data tag readingsystem;

[0011]FIG. 2 is a schematic diagram showing the components of themagnetic data tag reading system of FIG. 1 in more detail;

[0012]FIG. 3 is a schematic diagram showing details of the signalprocessor/controller illustrated in FIGS. 1 and 2;

[0013] FIGS. 4 and 5 illustrate the receive coil set;

[0014] FIGS. 6 and 7 illustrate the transmit coil set;

[0015]FIG. 8 illustrates the antenna comprising transmit and receivecoil sets;

[0016]FIG. 9 is a flow chart illustrating the overall processingalgorithm; to FIG. 10 is a schematic diagram of data acquisitioncircuitry;

[0017]FIG. 11 illustrates the transmit current waveforms;

[0018]FIG. 12 illustrates a flow chart for the signal processing andfiltering algorithm;

[0019]FIG. 13 illustrates signals at the inputs to the ADC from the x, yand z receiver coil preamplifiers, for a single element transition;

[0020]FIG. 14 illustrates the composite filter output of the signal inFIG. 13;

[0021]FIG. 15 illustrates a 3D scatter plot of the filtered receivervectors;

[0022]FIG. 16 illustrates a flowchart for the clustering algorithm usedfor planar tags;

[0023]FIG. 17 illustrates the composite filter output for three parallelelements;

[0024]FIG. 18 illustrates a flowchart for a parallel element clusteringalgorithm;

[0025]FIG. 19 illustrates a 3D scatter plot of the transition fieldvectors for a single element;

[0026]FIG. 20 illustrates the same 3D scatter plot as FIG. 19, tiltedsuch that the transition planes are edge-on;

[0027]FIG. 21 illustrates distribution of field vectors that occur alonga misaligned element direction vector; and

[0028]FIG. 22 illustrates a flowchart for the calculation of the meanswitching field, switching field variance, coercivity and DC bias field.

DETAILED DESCRIPTION

[0029] Referring to FIG. 1, a magnetic tag reading system comprises amagnetic data tag 1, an interrogation unit 2 and a signalprocessor/controller 3. Magnetic tags 1 to be used with a magnetic tagreader according to the invention can record information by means ofelements of differing coercivities, local bias fields and responseamplitudes, as well as orientation. This includes tags described in PCTpublication number W099/35610, as well as tags described in, forexample, U.S. Pat. No. 5,204,526, U.S. Pat. No. 5,729,201 andW098/26312. In general terms, magnetic tags 1 comprise magnetic elementswhich typically switch magnetisation state, for example magnetisationdirection, at given values of applied field depending on elementproperties, for example coercivity. These elements include, for example,thin film elements, bistable elements, Barkhausen wire elements andhigh-permeability elements. The applied field which causes switchingdepends on the magnitude of the component of the interrogation fieldvector in the direction of the element.

[0030] Referring to FIG. 2, the tag 1 is attached to an item beinglabelled or tagged 4, and is placed within an interrogation volume 5within the interrogation unit 2. The interrogation unit 2 includes anantenna 6, which comprises transmit and receive coil sets 7, 8. The tag1 is interrogated by a scanning magnetic field 9 generated by thetransmit coil set 7 under the control 10 of the processor/controller 3.In response to the interrogating magnetic field 9, the tag 1 generates adetectable magnetic field response 11, which is detected by the receivecoil set 8. The processor/controller 3 receives input signals 12, 13from the transmit and receive coil sets 7, 8 respectively and processesthe signals to decode data stored on the tag, which is made available atan output 14.

[0031] Referring to FIG. 3, the processor/controller 3 comprises awaveform generator for driving the transmit coil set 7, data acquisitioncircuitry 16 for receiving respective input signals 12, 13 from thetransmit and receive coil sets 7, 8 and a digital signal processor 17for processing the resulting output signals 18 from the data acquisitioncircuitry 16 to provide the decoded tag data 14.

[0032] The transmit and receive coil set arrangement 7, 8 is describedin detail by reference to FIGS. 4 to 8.

[0033]FIGS. 4 and 5 illustrate the receive coil set 8. The receivercoils are constructed on a cylindrical former 20 of diameter 200 mm andlength 400mm. FIG. 4 illustrates the three sets of orthogonal coils usedto couple with the tag magnetic elements within the interrogation zone.For the y-direction, the receiver coil set comprises 4 coils 21, 22, 23,24. Inner coils 22, 23 lie on the former 20 and extend 120 mm along thex-direction 25. Both inner coils 22, 23 comprise 100 turns 0.4 mm ecw.The outer coils 21, 24 comprise 58 turns of 0.4 mm ecw and are wound ona S second co-axial former (not shown) 260 mm in diameter. The coilsextend 156 mm along the x-direction. The four coils 21, 22, 23, 24 areconnected in series in the electrical sense illustrated and ‘balanced’by small mechanical re-alignments to achieve zero sensitivity to auniform magnetic field. A second receiver coil set as illustrated issensitive to tag generated field in the z-direction. This coil set isidentical to the coils 21, 22, 23, 24 but rotated through 90° as shown.The third coil set sensitive to tag generated field in the x-directioncomprises two solenoid coils 26, 27. The inner coil 26 comprises 100turns 0.4 mm ecw wound on the former 20, and is 120 mm long. The outercoil 27 comprises 58 turns of 0.4 mm ecw wound on the second 260 mmdiameter co-axial former and is 156 mm long. FIG. 5 illustrates all thecoils wound on the inner former 20, and the outer former 28.

[0034]FIG. 6 illustrates the three orthogonal transmit coilsconfiguration 7. The coils are wound on a cylindrical former 30, 370 mmlong and 300 mm diameter. A uniform magnetic field in the y-direction isproduced by four coils 31, 32, 33, 34. First and third coils 31, 33comprise a ‘modified Helmholz’ arrangement similar to coils 15 and 16.Second and fourth coils 32, 34 comprise a second modified ‘Helmholz’arrangement, with a magnetic axis 25° offset from the first and thirdcoils 31, 33. The two ‘modified Helmholz’ coil sets have magnetic axes12.5° either side of the y-direction. The first coil 31 comprises 50turns 1.4 mm ecw and extends 370 mm in length along the former. Wherethis coil 31 connects across the open end of the former 30, the coil isa flattened half circle with the total coil aperture width of 570 mm.The two edges of the coil 31 that lie along the solenoid (x-direction)subtend 120° at the axial centre of the former. Second to fourth coils32, 33, 34 are identical in size and form. Their orientation around theformer 30 is described above. The four coils are connected in series inthe sense illustrated. A second transmit coil set generates uniformfield in the z-direction. This set comprises four identical coilsorientated in an orthogonal direction as illustrated.

[0035] The final transmitter coil consists of a long solenoid coil 35comprising 260 turns of 1.4 mm ecw on the coil former. This generatesuniform field in the x-direction.

[0036]FIG. 7 shows the overall transmit coil arrangement for generatinguniform field in three orthogonal directions. FIG. 8 illustrates theantenna 6. The transmit coils on the former 30 are located co-axiallywith the receiver coil tube 20. The interrogation volume 5 is defined bya further 190 mm ID co-axial tube (not shown) that is used to define amechanical constraint on possible tag positioning in the antenna 6. Thelongitudinal region of highest sensitivity is less than 10 cm long andtags can be accurately read when separated by 10cm or more along theaxis of the reader tube.

[0037]FIG. 9 illustrates the overall sequence of steps required todecode data stored on a magnetic tag. The first stage is dataacquisition (step s1). Data is acquired by detecting the field 11resulting from the application of a scanning interrogation field 9 tothe tag 1, digitising the resulting signals and storing them forsubsequent processing. This results in 3 channels of input data, one foreach of the x, y and z directions. Digital signal processing is carriedout to identify individual switching points, also referred to herein astransitions (step s2). This results in an array of transitioninformation. Each transition is associated with an element (step s3) toprovide an array of elements. The elements are then individually decoded(step s4). Finally, the tag is decoded to provide tag value data (steps5).

Data Acquisition

[0038] Referring to FIG. 10, an example of the signalprocessor/controller 3 according to the invention comprises a NationalInstruments PCI6711 4-channel DAC card 39 for waveform generation and aNational Instruments PCI61 10E 4-channel ADC card 40 for dataacquisition. The cards are mounted into an industry standard IBMcompatible PC 41 running Windows 95™. The waveform generation card 39,under software control, generates three transmit excitation voltages 42,43, 44 which are passed through respective low-pass filters 45, 46, 47and amplified by respective power amplifiers 48, 49, 50 to driverespective orthogonal transmit coils, which are arranged in a seriesresonant configuration with respective capacitors 51, 52, 53 andresistors 54, 55, 56. The drive current is for example 3A rms togenerate a 2.5 kA/m interrogation field. The transmitter currents aremonitored by respective current sense resistors 57, 58, 59 which are fedthrough respective amplifiers 60, 61, 62 as inputs 63, 64, 65 to thedata acquisition card 40, where they are digitised at a sample rate of,for example, 160 kHz. The instantaneous transmit field vector can bedetermined from these three signals with knowledge of the relationshipbetween the transmit coil field and the current response. For example,pre-calibration of the system is carried out by measuring the transmitfield for different values of driving current.

[0039] Signals induced in the orthogonal receive coils are amplified byrespective amplifiers 66, 67, 68, filtered by respective 130 Hz notchfilters 69, 70, 71 to remove any transmit field component, and fed asinputs 72, 73, 74 to the data acquisition card, where they are digitisedat a sample rate of, for example, 160 kHz. The data acquisition isbuffered in such a fashion that data is clocked into a buffer, and readfrom the buffer asynchronously at some later point. The buffer depth issufficient to accommodate the worse-case latency in the subsequentprocessing step.

[0040] A continuous scan is used in this example to interrogate the tag,based on a nominal 130 Hz rotating magnetic field, whose normal vectoris arranged to trace out a spiral scan over the surface of a completesphere, tracing a path from one pole of the sphere to the other andback. The equations for the components of the ‘transmitted’ Binterrogation field are given by:

B_(x)=(cos²(φ)*cos(θ)+sin²(φ))*cos(ωt)+(sin(φ)*cos(φ)*cos(θ)−cos(φ)*sin(φ))*sin(ωt)

B_(y)=(cos(φ)*sin(φ)*cos(θ)−sin(φ)*cos(φ))*cos(ωt)+(sin²(φ)*cos(θ)+cos²(φ))*sin(ωt)

B _(z)=(−cos(φ))*sin(θ))*cos(ωt)−sin (θ)*sin(φ)*sin(ωt)

[0041] where t is the time, ω is the angular frequency of the 130 Hzscan, φ=(constant)* θ, and θ=cos⁻¹(1−t/T). T is the total time for onecomplete interrogation.

[0042]FIG. 11 shows the three transmit current waveforms 80, 81, 82received at the inputs 63, 64, 65 of the data acquisition card 40.

Digital Signal Processing

[0043] The digital signal processing stage (step s2) performed on thedata input to the data acquisition card 40 is now described withreference to the flow chart description of the processing algorithms inFIG. 12.

[0044] The purpose of the DSP algorithm is to identify individualtransitions, and to record all the relevant parameters on eachtransition for subsequent processing algorithms. This leads to a largereduction in the volume of data passed on to the subsequent processingstages.

[0045] The DSP algorithm operates on the three channels of sample dataproduced by the data acquisition process. FIG. 13 shows the raw impulseresponses in the x, y and z channels for a single transition.

[0046] Referring to FIG. 12, in a first step s10, an FIR filter isapplied to all three channels to produce three sets of filtered data,which form a receiver vector. The simplest filter consists of threerectangular sections, and provides a method of measuring the height ofthe peaks in the raw data. If the central section has width w and height+1, then the outer two sections have width w/2 and height −1. The width,w, is typically the same value as the response time of the magneticelement, for example, 20-30 μs.

[0047] The transmit field vector, H, is used to determine the correctpolarity of the element transition in each of the x, y and z receivercoils. The transition polarity in any receiver coil is directly relatedto the polarity of the rate of change of the field vector dH/dt in thedirection of the receiver coil. dH/dt values are used to produce a“polarity vector”, where each component can take the value ±1. Thescalar (dot) product of the polarity vector with the filtered receivervector is calculated (step s11) and the receiver vector magnitude, apositive number, is multiplied by the sign (±1) of the result (steps12). This results in the composite signal shown in FIG. 14, in whichthe polarity of transitions for every element is always the same,allowing the use of a simple peak detector to determine peak values.

[0048] Peak detection techniques are well known in the art. In thiscase, a simple threshold is used to gate the peak detector input data,to avoid noise appearing as spurious peaks. A peak is identified whenthree or more values exceed the threshold (step s13), and where thecurrent value is greater than both the previous and next value (steps14). The time of the peak is interpolated to a greater resolution thanthe sample frequency by a simple quadratic fit to these three points.

[0049] The data for each transition is stored in an array (step s15).The data includes:

[0050] Time

[0051] Field vector H)

[0052] Rate of change of field vector (dH/dt)

[0053] Receiver vectors (both raw and FIR filtered)

Element Association

[0054] The function of the element association algorithm is to associatetransition data points with particular magnetic elements in the tag.Subsequent processing steps can then analyse the data for each magneticelement in isolation, thereby reducing an apparently complex problemwith multiple elements into a series of relatively simple numericalsolves.

[0055] There are two primary mechanisms that are used to associatetransitions with elements, depending on whether the elements aregenerally parallel or not. These are described below. In the generalcase, the first step is to separate into groups using a non-parallelalgorithm, and then, if required, to analyse each separate group to seeif it contains more than one parallel or near-parallel elements.

[0056] For non-parallel elements, the filtered receiver vectors are usedto separate out the transitions between elements. This can be clearlyseen from FIG. 15, which shows the filtered receiver vectors in a 3Dscatter plot for an example tag having seven non-parallel elements.Inspection of the plot shows that the majority of the transition pointslie along one of 7 different lines through the origin, which indicatesthat there are 7 discernible directions of elements in the example tag.Each direction can be described by two parameters, and therefore thetransitions can be clustered together into groups in 2D. There are anumber of different appropriate techniques than can be used to achievethis multi-dimensional clustering (e.g. S. Makeig, S. Enghoff, T-P.Jung, M. Westerfield, J. Townsend, E. Courchesne and T. J. Sejnowski,“Moving-Window Independent Component Analysis of Event-Related EEG Data:Component Stability, Journal of Neurophysiology”). Additional knowledgeabout the particular tag construction can be useful to simplify theproblem. For example, if all the elements are in the same plane, thenthe problem can be reduced to a one-dimensional problem. Knowledge ofthe number of elements expected can assist in the clustering process.

[0057] In the particular case of a planar tag, with a known number ofelements, the algorithm outlined in FIG. 16 is used. The normal to theplane of the transitions is determined by, for example, a numericalprocess (step s20). For example, the dot product of every receivervector with an estimated direction vector is calculated, and thisprocess is iterated until the sum of the magnitude of the dot productsis minimised. This reduces the problem to a 1-D problem i.e. the anglein the plane.

[0058] An in-plane set of vectors can be calculated from the originalset of vectors simply by subtracting from each vector in turn the dotproduct of itself with the normal to the plane. In-plane angles betweenany two in-plane vectors can them simply be calculated in the usual wayusing dot products. All the in-plane angles are wrapped into the range0-180° by adding or subtracting multiples of 180° as required. Thealgorithm calculates a histogram of in-plane angles relative to somearbitrary datum, such as the first point. For example, if the histogrambins are 1° wide, then the nth bin will contain a count of the number ofangles that fall in the range n° to (n +1)°.

[0059] This will typically give a series of peaks, one for each element.For example, the algorithm obtains the second point from the transitionarray (step s21), measures the in-plane angle relative to the firstpoint (step s22) and increments the appropriate bin of the histogram(step s23). This process is repeated until all the data has beenprocessed (step s24). After applying Gaussian smoothing to the histogramdata (step s25), the direction of an element in the tag can be found bydetermining the highest peak in this histogram (step s26). To determinethe transitions that belong to the element in a given direction, thealgorithm finds all the transitions that are within, say, 2° (in plane)of this direction (step s27). The processed peak is then eliminated fromthe calculation (step s28) and this processing sequence is repeated(steps s26 to s28) until all the data has been processed (step s29).

[0060] To separate parallel elements, the algorithm makes use of twoproperties of a continuous scan of the field vector, H, around theelements, first that the elements transition in order from the lowest tothe highest coercivity and second, that the is field vector, H, rotatesby at least 90° between the last transition of the highest coercivityelement in one direction and the first transition of the lowestcoervicity element in the reverse direction.

[0061] If some of the elements do not change state, because the transmitfield does not reach a high enough value, then there will be fewertransitions, in a 180° scan, than there are elements. In this case,transitions are “lost”, starting with the highest-coercivity element.FIG. 17 shows the filtered composite waveform over a few rotations oftransmit field, for three parallel elements with different coercivities.Each element is associated with a respective peak 90, 91, 92 and it isrelatively straightforward to separate out the transitions belonging todifferent elements. An outline algorithm to achieve this is shown inFIG. 18.

[0062] This works by maintaining an element counter that is incrementedeach time a new transition is identified, and set to zero each time thefield rotates by more than 90° between transitions. Data is extractedfrom the transition array (step s30) and the algorithm determineswhether the transmit field has rotated by more than 90° since the lasttransition point (step s31). If it has, the element counter is reset tozero (step s32). Following this, the element number corresponding to thetransition is set according to the current value of the element counter(step s33). The element counter is then incremented (step s34) and theprocess repeated for the next transition point (step s30). For example,the first transition following the zeroing of the element counter isassociated with element 0, the next with element 1 and so on, until thefield has rotated by more than 90 degrees.

Element Decode

[0063] The purpose of the element decoding algorithm is to taketransition data belonging to one element, and to determine the best-fitdirection vector for this element. Once the direction is known, thecoercivity of the element, and any net DC field or “bias” along theelement vector can be calculated.

[0064]FIG. 19 is a 3D scatter plot of transition point field vectors,for a single bistable magnetic element with a finite coercivity. In thisexample, the field has been scanned approximately over the surface of asphere, so the transition points lie roughly on two circles 93, 94. Moregenerally, the transition points would be expected to lie on one of twoplanes. By tilting the view of the transition data in the scatter plot,it is possible to show the two planes edge-on, as illustrated in FIG.20. The bold vertical arrow 95 shows the element vector.

[0065] The element decoding algorithm attempts to determine the bestvector direction for the element, by minimising the scatter of fieldvectors resolved in this direction. FIG. 21 illustrates the situationwhere a guess 96 has been taken for the element vector that is not inthe correct direction. Taking the upper set of transitions 93, it isclear that when these are projected onto the element vector 96, theyform an extended distribution 97 (shown by a darkened section) along thevector 96. As the vector is rotated around, the extent of thisdistribution will be smallest when the vector is closest to the actualdirection of the tag element.

[0066]FIG. 22 shows a flowchart for the algorithm used to calculate theerror used in the iterative solving process. The algorithm uses thecurrent guess for the element vector direction, V. Initially, this isthe vector direction from the element association algorithm.

[0067] The first data point is retrieved (step s40) and the dot productof the direction estimate V with the polarity vector for dH/dt iscalculated, as described in relation to FIG. 12 above (step s41). Ifthis is positive (step s42) i.e. for the upper set of transitions, thenthe dot product of the field vector and the element vector is calculated(step s43) and added to the upper set of statistics (step s44). The dotproduct resolves the component of the field vector along the elementvector. The same calculation is carried out for the lower set oftransitions (steps s45, s46), indicated by the negative dot product atstep s41. The upper and lower (forward and reverse) sets of transitionsare distinguished by the sign of dH/dt along the direction of theelement, or alternatively by the sign of the filtered receiver vectoralong the direction of the element. This procedure is repeated for allthe data points (step s47). An average value of variance is calculatedfrom the variances for each of the upper and lower sets of transitionsseparately, weighted by the number of transitions in the upper and lowersets of transitions (step s48). A standard formula is used to calculatethe variance for each set of data. For a set of measured data points, x,the variance, var(x) is the mean of the squares of x minus the square ofthe mean of x, or mathematically

var(x)=(X ²)−(X)²

[0068] The weighted variance of N_(u) upper transition points, u, withvariance var(u) and N_(l) lower transition points, l, with variancevar(l) is then given by:${var} = \frac{{N_{u}{{var}(u)}} + {N_{l}{{var}(l)}}}{N_{u} + N_{l}}$

[0069] The weighted variance is used as a measure of the error in theguessed vector direction. When the guessed direction is equal to theactual element direction, the weighted variance will generally have itsminimum value. The value will never fall to zero, because there isalways a certain amount of noise in the determination of the transitionfield, arising from sources such as electronic noise and randomness inthe material behaviour. In the simplest case, the variance is a function(numerically evaluated, rather than an analytic function) of twodirection variables, such as θ and φ from the spherical polarco-ordinates (r, θ, φ). The value of this function can be minimisedusing a standard numerical minimisation algorithm. The variance variesapproximately quadratically with the deviation from the ideal direction,and this means that the minimisation algorithm can be extremelyefficient (the “quadratic” case is generally considered to be theeasiest). Multi-variate numerical minimisation algorithms are well knownin the art—for example, Powell's method.

[0070] When the weighted variance is not minimum (step s49), thedirection estimate V is adjusted in accordance with the appropriateminimisation algorithm (step s50) and the algorithm re-run with the newvalue of V. When the weighted variance is minimised, the mean values ofthe field for the upper and lower sets of transitions are calculated(steps s51, s52). The coercivity of the element is calculated as halfthe difference between the two switching fields (step s53), while the DCfield along the element is calculated as the sum of the two switchingfields (step s54).

[0071] Additional parameters as well as direction can usefully be addedto the numerical minimisation. The most important term to add is thevector velocity, which allows the algorithm to deal with the movement ofthe tag elements during the decoding process. The element direction insteps s41, s43, s45 is then a function of the time at which thetransition occurs, and the function for the variance then depends onfour parameters (for example θ, φ, dθ/dt and dφ/dt). Once again, thisfunction can simply be minimised using a standard multi-variateminimisation algorithm.

[0072] Many magnetic elements do not behave ideally, and showsignificant changes in their switching field (or coercivity) dependingon the value of dH/dt. A general form for the switching field,H_(switch), resolved along the element is:$H_{switch} = {H_{0} + {k_{a}( \frac{H}{t} )}^{a} + {k_{b}( \frac{H}{t} )}^{b} + \ldots}$

[0073] where a,b etc are arbitrary powers. If the coefficients k areknown, then the value of H₀ can be calculated from the measuredswitching field, and the variance of this value can be minimnised asbefore. If the coefficients k are not known, but the values a, b areknown, then the function for the numerical minimisation can also includethe coefficients, k, as function arguments, as well as the direction andvelocity terms. In this case, the values of k can be used to distinguishbetween different types of materials and thereby store more data.

[0074] Anisotropic thin-film magnetic materials can exhibit a furtherform of non-ideal behaviour. For materials with an easy-axis ofmagnetisation, the in-plane field perpendicular to the easy axis caninfluence the field at which the material switches. A similar approachto the one described above can be used to calculate a nominally constantvalue, H₀, from the raw switching points.

Tag Decode

[0075] The primary output data for each magnetic element from a readeraccording to the invention is as follows:

[0076] Orientation in the reader (vector)

[0077] Coercivity of the element (scalar)

[0078] Bias field along each element (scalar)

[0079] Amplitude response (scalar)

[0080] Secondary data for each element includes

[0081] dH/dt coefficients

[0082] Perpendicular field coefficients

[0083] Response time

[0084] Characteristic response “shape” or spectrum

[0085] Statistical distribution of primary parameters

[0086] This data assumes little about the construction of the tag. Thestructure of the tag (e.g. which elements share bias magnet elements)may be used to provide more detail—for example, the magnitude anddirection of an overall bias field. The details of the chosen codingscheme are used to translate all these raw parameters into useful datastored on the tag.

[0087] The above examples of the invention are intended to beillustrative, rather than restrictive. A person skilled in the art wouldunderstand that various modifications and variations in the detailedimplementation are possible, and are considered to be within the scopeand spirit of the invention as defined in the appended claims.

1. A method of reading a magnetic tag having at least one magneticelement, comprising: interrogating the tag with a scanning magneticfield; determining transition data associated with changes in themagnetization state of the at least one magnetic element; associatingthe transition data with one or more respective elements; and for eachelement, determining the element direction which corresponds to thetransition data for that element. 2-28 - cancelled.